Papadima, Stefan The rational homotopy of Thom spaces and the smoothing of isolated singularities. (English) Zbl 0563.57010 Ann. Inst. Fourier 35, No. 3, 119-135 (1985). Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and the question of its realization as a linear section (not necessarily hyperplane). MSC: 57R10 Smoothing in differential topology 32Sxx Complex singularities 55P62 Rational homotopy theory 32S05 Local complex singularities Keywords:smoothing of complex algebraic isolated singularities; topological smoothing; conical singularities; normal Chern degrees; rational homotopy of Thom complexes PDF BibTeX XML Cite \textit{S. Papadima}, Ann. Inst. Fourier 35, No. 3, 119--135 (1985; Zbl 0563.57010) Full Text: DOI Numdam EuDML References: [1] O. BURLET, Cobordismes de plongements et produits homotopiques, Comm. Math. Helv., 46 (1971), 277-288. · Zbl 0221.57017 [2] Y. FELIX, D. TANRE, Sur la formalité des applications, Publ. IRMA, Lille, 3-2 (1981). [3] H. HAMM, On the vanishing of local homotopy groups for isolated singularities of complex spaces, Journal für die reine und ang. Math., 323 (1981), 172-176. · Zbl 0483.32007 [4] R. HARTSHORNE, Topological conditions for smoothing algebraic singularities, Topology, 13 (1974), 241-253. · Zbl 0288.14006 [5] R. HARTSHORNE, E. REES, E. THOMAS, Nonsmoothing of algebraic cycles on Grassmann varieties, BAMS, 80(5) (1974), 847-851. · Zbl 0289.14011 [6] S. HALPERIN, J.D. STASHEFF, Obstructions to homotopy equivalences, Adv. in Math., 32 (1979), 233-279. · Zbl 0408.55009 [7] M.L. LARSEN, On the topology of complex projective manifolds, Inv. Math., 19 (1973), 251-260. · Zbl 0255.32004 [8] J. MILNOR, Singular points of complex hypersurfaces, Princeton University Press, 1968. · Zbl 0184.48405 [9] S. PAPADIMA, The rational homotopy of thom spaces and the smoothing of homology classes, to appear Comm. Math. Helv. · Zbl 0592.57025 [10] E. REES, E. THOMAS, Cobordism obstructions to deforming isolated singularities, Math. Ann., 232 (1978), 33-53. · Zbl 0381.57011 [11] H. SHIGA, Notes on links of complex isolated singular points, Kodai Math. J., 3 (1980), 44-47. · Zbl 0442.57015 [12] A.J. SOMMESE, Non-smoothable varieties, Comm. Math. Helv., 54 (1979), 140-146. · Zbl 0394.14016 [13] D. SULLIVAN, Infinitesimal computations in topology, Publ. Math. IHES, 47 (1977), 269-331. · Zbl 0374.57002 [14] R. THOM, Quelques propriétés globales des variétés différentiable, Comm. Math. Helv., 28 (1954), 17-86. · Zbl 0057.15502 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.